1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was e20b37f3e37581c0b92d3ef531ab866e72ebaee1.

2 Data

Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.

3 Basic Exploration

Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.

Reported Cases by Continent

Reported Cases by Continent

Below we plot the cumulative deaths by country on a log scale:

Reported Deaths by Continent

Reported Deaths by Continent

4 Method & Assumptions

The methodology is described in detail here. We filter out countries with populations of greater than 500 000. Weeks where the deaths or cases are not greater than 50 are left out of results.

5 Results

5.1 Current \(R_{t,m}\) estimates by country

Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.

5.1.0.1 Cases

5.1.1 Deaths

5.2 Top 10 countries

Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.

5.2.1 Lowest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Ecuador deaths 169 2020-10-21 0.4 0.4 0.5
Honduras deaths 54 2020-10-21 0.5 0.7 0.9
Philippines deaths 318 2020-10-21 0.6 0.7 0.8
Mexico deaths 2,473 2020-10-21 0.7 0.7 0.8
Bangladesh deaths 122 2020-10-21 0.7 0.8 0.9
Saudi_Arabia deaths 130 2020-10-21 0.7 0.8 0.9
Costa_Rica deaths 98 2020-10-21 0.7 0.9 1.0
India deaths 5,328 2020-10-21 0.9 0.9 0.9
Chile deaths 306 2020-10-21 0.8 0.9 1.0
Israel deaths 223 2020-10-21 0.8 0.9 1.0

5.2.2 Lowest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Israel cases 9,229 2020-10-21 0.5 0.5 0.5
Madagascar cases 56 2020-10-21 0.4 0.5 0.7
Botswana cases 570 2020-10-21 0.6 0.6 0.7
Jamaica cases 464 2020-10-21 0.6 0.7 0.7
Cote_dIvoire cases 159 2020-10-21 0.6 0.7 0.8
Trinidad_and_Tobago cases 206 2020-10-21 0.6 0.7 0.8
Bolivia cases 1,115 2020-10-21 0.7 0.7 0.8
Guyana cases 231 2020-10-21 0.6 0.7 0.8
Suriname cases 72 2020-10-21 0.6 0.8 0.9
Venezuela cases 3,253 2020-10-21 0.7 0.8 0.8

5.2.3 Highest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Italy deaths 459 2020-10-21 1.6 1.8 1.9
Germany deaths 198 2020-10-21 1.5 1.7 1.9
Croatia deaths 52 2020-10-21 1.2 1.6 2.1
Czechia deaths 513 2020-10-21 1.5 1.6 1.7
France deaths 952 2020-10-21 1.5 1.6 1.7
Jordan deaths 189 2020-10-21 1.4 1.6 1.8
United_Kingdom deaths 949 2020-10-21 1.5 1.6 1.7
Hungary deaths 236 2020-10-21 1.3 1.5 1.7
Bulgaria deaths 96 2020-10-21 1.2 1.5 1.8
Libya deaths 90 2020-10-21 1.2 1.4 1.7

5.2.4 Highest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Djibouti cases 71 2020-10-21 3.2 4.0 5.0
Cyprus cases 792 2020-10-21 2.3 2.5 2.6
Kosovo cases 935 2020-10-21 1.9 2.0 2.1
Switzerland cases 20,441 2020-10-21 1.9 1.9 1.9
Azerbaijan cases 3,498 2020-10-21 1.8 1.9 1.9
Italy cases 68,982 2020-10-21 1.7 1.7 1.7
Nicaragua cases 81 2020-10-21 1.4 1.7 2.0
Slovenia cases 5,248 2020-10-21 1.6 1.7 1.7
Georgia cases 7,016 2020-10-21 1.6 1.6 1.7
Bulgaria cases 6,089 2020-10-21 1.6 1.6 1.7

5.3 Country Plots by Continent

Below we plot results for each country/province in a list. We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds five.

5.3.1 Africa

5.3.1.1 Algeria

5.3.1.2 Angola

5.3.1.3 Benin

5.3.1.4 Botswana

5.3.1.5 Burkina_Faso

5.3.1.6 Burundi

5.3.1.7 Cameroon

5.3.1.8 Cape_Verde

5.3.1.9 Central_African_Republic

5.3.1.10 Chad

5.3.1.11 Comoros

5.3.1.12 Congo

5.3.1.13 Cote_dIvoire

5.3.1.14 Democratic_Republic_of_the_Congo

5.3.1.15 Djibouti

5.3.1.16 Egypt

5.3.1.17 Equatorial_Guinea

5.3.1.18 Eritrea

5.3.1.19 Eswatini

5.3.1.20 Ethiopia

5.3.1.21 Gabon

5.3.1.22 Gambia

5.3.1.23 Ghana

5.3.1.24 Guinea

5.3.1.25 Guinea_Bissau

5.3.1.26 Kenya

5.3.1.27 Lesotho

5.3.1.28 Liberia

5.3.1.29 Libya

5.3.1.30 Madagascar

5.3.1.31 Malawi

5.3.1.32 Mali

5.3.1.33 Mauritania

5.3.1.34 Mauritius

5.3.1.35 Morocco

5.3.1.36 Mozambique

5.3.1.37 Namibia

5.3.1.38 Niger

5.3.1.39 Nigeria

5.3.1.40 Rwanda

5.3.1.41 Senegal

5.3.1.42 Sierra_Leone

5.3.1.43 Somalia

5.3.1.44 South_Africa

5.3.1.45 South_Sudan

5.3.1.46 Sudan

5.3.1.47 Togo

5.3.1.48 Tunisia

5.3.1.49 Uganda

5.3.1.50 United_Republic_of_Tanzania

5.3.1.51 Western_Sahara

5.3.1.52 Zambia

5.3.1.53 Zimbabwe

5.3.2 America

5.3.2.1 Argentina

5.3.2.2 Bolivia

5.3.2.3 Brazil

5.3.2.4 Canada

5.3.2.5 Chile

5.3.2.6 Colombia

5.3.2.7 Costa_Rica

5.3.2.8 Cuba

5.3.2.9 Dominican_Republic

5.3.2.10 Ecuador

5.3.2.11 El_Salvador

5.3.2.12 Guatemala

5.3.2.13 Guyana

5.3.2.14 Haiti

5.3.2.15 Honduras

5.3.2.16 Jamaica

5.3.2.17 Mexico

5.3.2.18 Nicaragua

5.3.2.19 Panama

5.3.2.20 Paraguay

5.3.2.21 Peru

5.3.2.22 Puerto_Rico

5.3.2.23 Suriname

5.3.2.24 Trinidad_and_Tobago

5.3.2.25 United_States_of_America

5.3.2.26 Uruguay

5.3.2.27 Venezuela

5.3.3 Asia

5.3.3.1 Afghanistan

5.3.3.2 Bahrain

5.3.3.3 Bangladesh

5.3.3.4 Bhutan

5.3.3.5 China

5.3.3.6 India

5.3.3.7 Indonesia

5.3.3.8 Iran

5.3.3.9 Iraq

5.3.3.10 Israel

5.3.3.11 Japan

5.3.3.12 Jordan

5.3.3.13 Kazakhstan

5.3.3.14 Kuwait

5.3.3.15 Kyrgyzstan

5.3.3.16 Lebanon

5.3.3.17 Malaysia

5.3.3.18 Maldives

5.3.3.19 Myanmar

5.3.3.20 Nepal

5.3.3.21 Oman

5.3.3.22 Pakistan

5.3.3.23 Palestine

5.3.3.24 Philippines

5.3.3.25 Qatar

5.3.3.26 Saudi_Arabia

5.3.3.27 Singapore

5.3.3.28 South_Korea

5.3.3.29 Sri_Lanka

5.3.3.30 Syria

5.3.3.31 Taiwan

5.3.3.32 Tajikistan

5.3.3.33 Thailand

5.3.3.34 Turkey

5.3.3.35 United_Arab_Emirates

5.3.3.36 Uzbekistan

5.3.3.37 Vietnam

5.3.3.38 Yemen

5.3.4 Europe

5.3.4.1 Albania

5.3.4.2 Armenia

5.3.4.3 Austria

5.3.4.4 Azerbaijan

5.3.4.5 Belarus

5.3.4.6 Belgium

5.3.4.7 Bosnia_and_Herzegovina

5.3.4.8 Bulgaria

5.3.4.9 Croatia

5.3.4.10 Cyprus

5.3.4.11 Czechia

5.3.4.12 Denmark

5.3.4.13 Estonia

5.3.4.14 Finland

5.3.4.15 France

5.3.4.16 Georgia

5.3.4.17 Germany

5.3.4.18 Greece

5.3.4.19 Hungary

5.3.4.20 Ireland

5.3.4.21 Italy

5.3.4.22 Kosovo

5.3.4.23 Latvia

5.3.4.24 Lithuania

5.3.4.25 Luxembourg

5.3.4.26 Moldova

5.3.4.27 Montenegro

5.3.4.28 Netherlands

5.3.4.29 North_Macedonia

5.3.4.30 Norway

5.3.4.31 Poland

5.3.4.32 Portugal

5.3.4.33 Romania

5.3.4.34 Russia

5.3.4.35 Serbia

5.3.4.36 Slovakia

5.3.4.37 Slovenia

5.3.4.38 Spain

5.3.4.39 Sweden

5.3.4.40 Switzerland

5.3.4.41 Ukraine

5.3.4.42 United_Kingdom

5.3.5 Oceania

5.3.5.1 Australia

5.3.5.2 New_Zealand

5.3.5.3 Papua_New_Guinea

## Detailed Output

Detailed output for all countries are saved to a comma-separated value file. The file can be found here.

6 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed serial interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The serial interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] European Centre for Disease Prevention and Control, “Data on the geographic distribution of COVID-19 cases worldwide.” European Union, 2020 [Online]. Available: https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide